Problem: Rewrite as a simplified fraction. ${0.5\overline{8} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 58.8888...\\ 10x &= 5.8888...\end{align*}}$ Subtracting the two equations, we have: ${90x = 53}$ ${x = \dfrac{53}{90}} $